Parameter optimization for linear equations.

Hi, Which matlab function/method should I used to find possible solutions to satisfy following equations?

0.213 = x1*exp(-y1/98000);

0.012 = x2*exp(-y2/98000);

0.163 = x3*exp(-y3/98000);

0.152 = x4*exp(-y4/98000);

10^6 < x < 10^13;

70 < y < 150;

regards

Steve

Answer 1

[Matt J]

You could probably do this by hand or with basic MATLAB arithemtic. Taking the log of both sides of the equations and making the change of variables z=log10(x) transforms this to

log10(LHS)=z-y/98000

6<=z<=13
70<=y<=150

Notice that the equality is just the equation for a line. It is fairly simple arithmetic to figure out where a single line satisfies a set of inequalities. If you want to automate it slightly, you can use this function

http://www.mathworks.com/matlabcentral/fileexchange/30892-representing-polyhedral-convex-hulls-by-vertices-or-inequalities

Because the above is a system of linear equalities and inequalities, the LCON2VERT function at this link will tell you the vertices of the line segment they describe.